Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.
But the notion of changing brain waves is a very appealing one, from a marketing stand point. People can visualize brain waves and we like synchrony. Also, in the computer age, we understand the notion of “programming.” We also have been prepped for the future by movies such as The Matrix, where people could master Kung Fu in minutes by simply “downloading” the knowledge. This gives the whole notion a superficial plausibility. But the science just isn’t there.
This research investigates the brainwave entrainment process and aims to demonstrate the usefulness of such an approach within the framework of cognitive performance improvements. In the introductory part the theories regarding the neurophysiological structure and the psychological processing of the cognitive system are discussed, for each of their components that are considered to be relevant for this research. The hypothesis states that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition. The research variables are the cognitive performance (the dependent variable) and the brainwave entrainment (the independent variable). The brainwave entrainment program consists in the synchronized application of Alpha binaural beats and stroboscopic light, at a 10.2 Hz frequency, in a 30 minutes long session. The difference was made by the stroop effect based exercise that was used as a frame. There were 60 participants, divided into two independent samples. The two independent samples t test for the means differences was used in the statistical analysis. The obtained results by evaluations and by statistics confirmed this research's hypothesis, stating that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition.
Participants in the included studies were children and adults, either healthy or with conditions such as learning disabilities, attention deficit hyperactivity disorder, migraine, stress, anxiety and myofascial pain. Interventions included single, alternating, ascending or descending frequencies of photic or auditory stimulation or audiovisual entrainment selected either by the participant or by the investigator. Nearly half the studies used single sessions and the rest used multiple sessions ranging from nine to 100. Length of session varied from 0.5 seconds to 60 minutes. Frequency of session varied from twice daily to weekly. Outcomes reported in the review included cognition (including verbal skills, performance skills, attention, memory and overall intelligence/achievement), short- and long-term stress, pain, headache/migraine, mood, behavioural problems and premenstrual syndrome (PMS).
As strange as it may sound, vocal toning is a special technique that reduces the stress hormones adrenaline and cortisol. Try sneaking off to a quiet place to spend a few minutes toning before a meeting with your boss and see how much more relaxed and focused you feel. It works by exercising the tiny muscles of the inner ear that help you detect the higher frequencies of human speech that impart emotion and tell you what someone is really trying to say. Not only will you feel more relaxed in that meeting, you’ll also be better able to understand what he’s trying to communicate.

Brain Wave Entrainment is any procedure that causes one's brainwave frequencies to synchronize with a periodic stimulus (sound, vibration or light) having a frequency corresponding to the intended brain-state (for example, to induce a trance, dreams, sleep or relaxation.) It is also called the Flicker-response because of how staring at a campfire or the flickering of a burning candle can lull you into a state of calmness and serenity. There was an extensive article on this phenomenon by Gerard Oster in Scientific American in 1973. It may sound novel, but in many ways, this is old tech.

A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion:
I enjoy this one called: Cognition Enhancer For Clearer and Faster Thinking – Isochronic Tones (Electronic) … I seem to enjoy it. Any harm in just listening to this one every day for 30 minutes as a routine daily thing, just like brushing your teeth and making your bed. I would just use it at times when I’m working at my desk, maybe even reading the online news etc…Thoughts?
Neural oscillations are rhythmic or repetitive electrochemical activity in the brain and central nervous system. Such oscillations can be characterized by their frequency, amplitude and phase. Neural tissue can generate oscillatory activity driven by mechanisms within individual neurons, as well as by interactions between them. They may also adjust frequency to synchronize with the periodic vibration of external acoustic or visual stimuli.[3]